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Measurement-based quantum computation on symmetry breaking thermal States
Keisuke Fujii1, Yoshifumi Nakata2, Masayuki Ohzeki3
1Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
Physical Review Letters
|August 29, 2014
Summary
Measurement-based quantum computation (MBQC) is more robust against thermal noise in interacting cluster states. Long-range order in thermal states below a critical temperature enhances MBQC stability, even at higher temperatures.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
Background:
- Measurement-based quantum computation (MBQC) is a leading model for quantum computing.
- Thermal states and phase transitions in quantum systems pose challenges for robust computation.
- The cluster Hamiltonian is a key resource state for MBQC.
Purpose of the Study:
- To investigate the impact of thermal phase transitions on MBQC robustness.
- To explore the role of long-range order in symmetry-breaking thermal states for quantum computation.
- To determine the potential for performing MBQC at higher temperatures using interacting Hamiltonians.
Main Methods:
- Analysis of the interacting cluster Hamiltonian and its thermal phase transitions.
- Studying the properties of thermal states below a critical temperature.
- Investigating the robustness of MBQC against thermal excitations in 2D and 3D systems.
Main Results:
- Long-range order in symmetry-breaking thermal states significantly enhances MBQC robustness.
- MBQC exhibits enhanced stability in 2D systems with interacting cluster states.
- Topological protection of MBQC is proven in 3D systems below the critical temperature.
- The interacting cluster Hamiltonian enables MBQC at temperatures one order of magnitude higher than the free cluster Hamiltonian.
Conclusions:
- Interacting cluster Hamiltonians offer a pathway to robust quantum computation in the presence of thermal noise.
- Symmetry-breaking thermal states with long-range order provide inherent protection for MBQC.
- These findings pave the way for practical quantum computation at elevated temperatures.
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